Construction and Performance of Quantum Burst Error Correction Codes for Correlated Errors

TL;DR

This paper develops a formalism for quantum burst error correction codes (QBECC), derives bounds, proposes new constructions, and demonstrates their superior performance over standard quantum error correction codes in correlated error scenarios.

Contribution

It introduces the quantum Reiger bound for QBECCs, proposes two new construction methods, and shows these codes outperform existing codes under correlated errors.

Findings

New QBECCs with improved parameters

Some codes saturate the quantum Reiger bounds

QBECCs outperform standard QECCs in correlated error channels

Abstract

In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat such error patterns in the quantum regime. Our contributions are as follows. Firstly, we derive an upper bound for the correctable burst errors of QBECCs, the quantum Reiger bound (QRB). This bound generalizes the quantum Singleton bound for standard quantum error correction codes (QECCs). Secondly, we propose two constructions of QBECCs: one by heuristic computer search and the other by concatenating two quantum tensor product codes (QTPCs). We obtain several new QBECCs with better parameters than existing codes with the same coding length. Moreover, some of the constructed codes can saturate the quantum Reiger bounds. Finally, we perform numerical experiments for our constructed codes over Markovian correlated depolarizing quantum memory channels, and show that QBECCs indeed outperform standard QECCs in this scenario.